Question 1 Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations.

The following stemplot shows the swimming speeds, in kilometers per hour (km/h), for a random sample of 31 emperor penguins.

The figure presents a stemplot labeled, Speed, in kilometers per hour. The key indicates 7, vertical line, 8 equals 7.8. The data in the graph are as follows. The table has 9 rows of data. The rows are as follows. Row 1: first column 7, second column 8. Row 2: first column 8, second column 3, 4. Row 3: first column 8, second column 6, 7, 9. Row 4: first column 9, second column 0, 0, 1, 3, 4. Row 5: first column 9, second column 5, 5, 6, 7, 8, 8, 9. Row 6: first column 10, second column 0, 1, 1, 2, 3. Row 7: first column 10, second column 5, 8, 8, 8. Row 8: first column 11, second column 0, 2, 3. Row 9: first column 11, second column 5.
(a) The mean of the sample is 9.771 km/h, and the standard deviation is 0.944 km/h. Construct and interpret a 95 percent confidence interval for the mean swimming speed of all emperor penguins in the population.

Question 2
(b) Can the estimate of the mean swimming speed be generalized to all types of penguins? Explain your reasoning.